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03-31-2002, 07:57 PM | #11 | |
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It seems to me that if the laws of noncontradiction and identity are "true", they are necessarily true always and everywhere. A is never "not-A". A cannot be both A and B at the same time and in the same relation. These are certainly contextual, so no problem there, but is there ever a context in which they could not be true? If not, how can these axioms fail to be absolute truths? Regarding your example of "continuities", it seems to me that all you've done is push the "absolute" back a step. In order to derive the A-B-C relationship as you do, one must assume the truth of induction. But if induction is not "absolutely" true, how is "repeated experimentation" of any value? Regards, Bill Snedden |
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03-31-2002, 10:14 PM | #12 | ||||||||||||||||
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Sorry for the late post, Kim.
I'm unusually busy this weekend with offline matters. Bill Snedden has already anticipated my reply and has stated it in a manner much more eloquently than I did, but I'll post what I had typed up originally anyway. Quote:
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Quantum observations, in that case, would provide a good reason not to make a distinction between "natural truths" and "abstract truths", and would render all truths (including "context-limited truths") uncertain. In that case, we could never be certain enough about the world to say that anything is "true" at all. Furthermore, would the statement that "no truth can be true in all contexts" be itself a "context-limited truth"? If it is not, then it exists as at least one absolute truth (opening the door for others). But if it is a "context-limited truth" then it is circular for the same reason that you argued that the claim that it is self-refuting to say there is no absolute truth, is circular. Quote:
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[ April 01, 2002: Message edited by: jpbrooks ]</p> |
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03-31-2002, 11:11 PM | #13 | ||
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Let's try a bit of a thought experiment. Mathematics, logic, scientific theories, are really just philosophical models. They have their own sets of assumptions, rules, and definitions. There are other possible philosophical models of the same type. In fact, the only practical limit to them, is that they all must be internally consistent. All you really need to do, to create a second philosophical model that cannot be reconciled with the first, is to start with an underlying assumption that is incompatible with the underlying assumption of the first model. Your new model could be consistent within itself, so any statement you logically derive from this model would be true within its context, but it might be false from the point of view of the first model. It is true that very many such models might not be very consistent with observed reality, but what if some of them are? And what happens in those circumstances where consistency with the natural world is not very important? (e.g. the rules of chess compared to the rules of chequers.) You'd think that 8+8=16 is a pretty good contender for an indisputably true axiom -- one that would never find itself in a context where it was not true. But if you were to ever formulate a new kind of mathematics, whose underlying assumptions were different from and incompatible with ordinary mathematics, then such a context -- where 8+8 does not equal 16 -- could indeed exist. And if you were to argue that no one could or would invent such a new kind of mathematics, then you would be wrong, because someone did invent it, and it's called Modulo. Modulo not only exists, but it is a very useful and necessary branch of mathematics, even though its underlying assumptions are incompatible with standard mathematics. Standard mathematics assumes that the set of numbers is infinite, and that they don't repeat. Modulo assumes that the set of numbers is finite, and that they do repeat. Modulo is the kind of mathematics you would do on a clockface, or a calendar. In Mod12, 8+8 does not equal 16, rather, 8+8=4. If you can't even be absolutely sure that 8+8=16, then what can you be sure about? Now, LinuxPup wants to bury the idea of context sensitivity, by incorporating it into his "absolute truth" statements. In my philosophical system, I would prefer not to -- I would rather keep context out in the open, where it's not going to be forgotten so easily. Quote:
So basically, what I have done is introduced a new mechanism. When it comes to the most basic and fundamental questions, I prefer to minimize my reliance on deduction. So, I scan my perceptual environment and my memory of experience looking for continuities. I notice that when I put one object with another object, then there are always two objects. That it is a continuity. Once I am satisfied that it is truly a continuous phenomenon -- that it happens every time -- then I don't bother testing it anymore, and in that way it becomes an abstract truth. The only deduction I have to make is that if I've observed the same result every time I test it, then it will probably go on happening that way. You will notice too, that I do not insist that this deduction is 100% accurate. I know that I can switch on a light switch 99 times and the room will be flooded with light. But I also know that the hundredth time I flick the switch, the lightbulb might go *plink* and the room might stay in darkness. I accept these vagueries as an unavoidable part of being human. [ April 01, 2002: Message edited by: Kim o' the Concrete Jungle ]</p> |
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04-01-2002, 05:56 AM | #14 | ||||
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I'm not exactly sure what "reasonable doubt" might be, but I believe that I can show by retortion that it is impossible to falsify the law of noncontradiction (Lnc). While this doesn't prove it true beyond any doubt, it would certainly seem more reasonable than not to accept it as true based on such an argument. If Lnc is true, statements of the type "X is true" are either true or false. Conversely, if Lnc is false, statements of the type "X is true" may be both true AND false simultaneously. Therefore, it is impossible to both deny the truth of Lnc and demonstrate the truth of that statement. Therefore, it is impossible to demonstrate the falsity of Lnc because any attempt to do so must necessarily assume the truth of Lnc and therefore is self contradictory. Is it not more reasonable to believe Lnc to be absolutely true? Quote:
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8+8=16 is not an axiom at all. Neither is 1+1=2. These symbolic representations are themselves based on axioms: the Peano postulates. And, as it turns out, these axioms also seem to be true in any formulation of mathematics, base 10, base 9, or Modulo. So, actually what we have is a set of "truths" that appear to remain true, regardless of context. That is, 8+8=16 in base 10, 8+8=17 in base 9, or 8+8=4 in Modulo 12 are only manipulations of mathematical symbols in differing mathematical models all of which follow from the basic truths of the Peano postulates. Quote:
Regards, Bill Snedden |
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04-01-2002, 07:51 AM | #15 |
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"1. We receive sense data x that informs us about an entity A. x is thus the representation of A.
2. We receive sense data x' that informs us about an entity A'. x' is thus the representation of A' 3. By internally storing/transmitting the data x and x' they can be compared. 4. If these data are sufficiently alike, our comparison/detection process will have deemed that A and A' are identical. 5. This 'identicalness' result/assumption is "a truth"." If someone disagreed with this comparison, that you draw a truth statement from, because they could not draw the same comparison, what grounds would you have for deciding between the case that a truth statement could be drawn and the case that a truth statement couldn't? Could you both be telling truths, only the truths are relative to the means with which you use to discern sufficiently similar relationships between A and A'? Or might one of you be wrong? If not, how does this rule objective truth out, only the argument states how we arrive at truth statements, without reasoning why this precludes being able to make objectively true statements, beyond asserting that we sense things. Sensing A and A' seems to rule out our ability to achieve objective truth. I can see no other line of reasoning that would rule it out such that your conclusion is fully supported. I do believe the problem is getting beyond x and x' when making the comparison, but would you agree that it is either the case that A is or is not the same as A' via the law of the excluded middle? Perhaps we therefore can't know beyond x and x' what the answer is, but does that mean there is no answer beyond x? i.e. is it impossible to assert that there must be some comparison or contrast in itself, waiting for us to discover it. My thinking is that if this is so, then a statement might actually be objectively true with regard to A and A'. I'm rehashing our interesting dialogue on another thread, I wish I could add more, but I think I'm stumped on the issue of whether if we reduce truth to statements we make that arise out of satisfactory identity between A and A' (whatever they are) then we are denying that there is a state of the universe with regard to A and A', and that state is itself and not another state. Just because we can't get out from x and x' doesn't mean there isn't a particular and unequivocal relationship between A and A'. Are you suggesting we'll never get closer than our sensory representations and we therefore can't know if they actually do describe an identity? Adrian |
04-01-2002, 08:24 AM | #16 | ||||||||||||
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Kim o' the Concrete Jungle: First I'd like to say that you never answered point 1 of mine, so I'll restate it: Quote:
Please answer this question without trying to get around it. Quote:
Belief does not create reality. Quote:
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Heh, don't evade my question on point 5. You tried to switch it to spherical geometry, which is why I forced the context to a flat 2 dimensional surface. So now answer my question: Do you believe that (1/2)(base)(height) = Area of a triangle in euclidean geometry? In every case? Don't evade the question, show me an exception where this is not true. I have shown earlier that your rebuttal to point 6 is false. I am still waiting for proof that absolute truth does not exist. Quote:
I have a class, I'll continue later.... |
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04-01-2002, 09:52 AM | #17 | |||||||||||||||
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"[Quentin] Smith seeks rectify this defect in his argument, however, by pointing out that the Uncertainty relation also permits energy or particles (notably virtual particles) to "spontaneously come into existence" for a very brief time before vanishing again. It is therefore false that "all beginnings of existence are caused" and, hence, ". . . the crucial step in the argument to a supernatural cause of the Big Bang . . . is faulty" (pp. 50-51). But as a counterexample to (1'), Smith's use of such vacuum fluctuations is highly misleading. For virtual particles do not literally come into existence spontaneously out of nothing. Rather the energy locked up in a vacuum fluctuates spontaneously in such a way as to convert into evanescent particles that return almost immediately to the vacuum. As John Barrow and Frank Tipler comment, ". . . the modern picture of the quantum vacuum differs radically from the classical and everyday meaning of a vacuum-- nothing. . . . The quantum vacuum (or vacuua, as there can exist many) states . . . are defined simply as local, or global, energy minima (V'(O)= O, V"(O)>O)" ([1986], p. 440). The microstructure of the quantum vacuum is a sea of continually forming and dissolving particles which borrow energy from the vacuum for their brief existence. A quantum vacuum is thus far from nothing, and vacuum fluctuations do not constitute an exception to the principle that whatever begins to exist has a cause." So to answer your question, no it doesn't violate the law of conservation of energy, and *if* it did, that would mean the "law" of conservation of energy is false, that is, not a law at all. This would be a human error of understanding, not a violation of truth, which by definition cannot be violated. Quote:
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"No." "Did you run an hour ago?" "Yes." You might say "See, here is an example of a relative truth." But the problem is, the two questions you asked me are just that, two seperate questions referring to different cases. It is absolutely false that I ran yesterday, but it is absolutely true that I ran an hour ago. Now concerning the statement, "I ran", which seems vague at best: Regardless of how vague or easy it is to twist what I said, the fact would remain, and remain absoultely, that I ran an hour ago. All the contexts are not given my sentence "I ran" (who am I, where did I run to, for how long, etc.), but that doesn't mean they don't exist. Yes truth must have context, and that's what makes truth absolute. Quote:
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So to answer your question: Yes I rely on the assumption that absolute truth exists to prove that absolute truth exists. This does not make the argument invalid, on the contrary, I cannot make any argument, unless I believe in truth. The fact is, you, Kim o' the Concrete Jungle, believe in absolute truth, you just won't admit it. How do I know this? Because you've been using it in *every* argument you give. When you essentially say, "you're wrong, I'm right concering this issue", your making a truth claim. Now if it's not absolute, then when is your argument wrong? You've been dancing around this issue, and have not attempted to deal with it. Deal with it. |
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04-01-2002, 12:22 PM | #18 | ||||
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If someone disagreed, they would not be able to participate/share in the same instance of "truth". In this sense, truth can be arbitrary - for example one man may deem an animal to be a (true) horse, while another may deem it to be a (true) mule. Note 1: In considering your two observers M and N you might be tempted to consider the external object A common to both. To avoid the idealist's criticism, M should observe A and A' through sense data x and x' while N should observe B and B' through sense data y and y'. Through "common" observation and communications M and N can negotiate further coordinates, points of reference etc. to ensure they are sensing the same external phenomenon. Conclusion, truth/identity relations are assigned (subjectively and internally) by individuals according their internal concepts describing reality. Note 2: Numbers are a specialized concept because they use "pre-determined" (i.e. part of their definition) homogeneity between the units or sub-units of a numbering system. So, should M and N disagree that the abstract idea of 1 + 1 is 2, maybe N says this is 10 because of using binary. So, in the case of math, what might look like an absolute truth is just the definition of relations between (abstract) quantities. Quote:
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What I'm really driving at is if you strictly obey the Law of Identity your concept of reality can be no other way! This is perhaps why Russell got stuck with his Antinomy - a set cannot be a member of itself without violating the law of identity (unless, perhaps, it was the only member of its set but then it wouldn't be a set etc.). If you're into that stuff take a look at my <a href="http://www.reconciliationism.org/god_theorem.htm" target="_blank">God Theorem</a>. Everything is different and all we can do is compare these differences - Catch 22! Please feel free to try and shoot this down (now there's an invitation) - its the leading edge of where I'm at with reality. Cheers! |
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04-01-2002, 06:05 PM | #19 |
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I look at the latest batch of responses and I despair.
LinuxPup, how many times have I explained and given examples of what I mean by "context", and how context limits the applicability of any "true" statement? And yet, even now, you're still ignoring it. If you can't step outside of your own peculiar little batch of "absolutist" assumptions even for a single moment, then you won't even understand what I'm talking about, let alone provide a meaningful critique of it. <img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" /> I give up on you. If you're not even prepared to try, then I'm not going to waste another minute on you. Bill Snedden, just replace the word "axiom" with the word "statement" in my 8+8=16 example, and that will be closer to what I meant. John Page, I pretty much agree with everything you said in your first post. I was a bit dubious about that word "identical", but I can accept your special definition of the term. What you present is one possible model of truth, mine is another possible model, LinuxPup's is a third. From my point of view, it is absurd to try and prove one model true and all the other models false. According to my own philosophical position (i.e. context), they are all possible models, only some might be more "useful" than others. (And I have a specific criterion of "usefulness", in the same way you have a specific definition of "identical".) To everyone: I mentioned this in the opening paragraphs of this thread, but I think it bares repeating. The model of truth I am attempting to formulate is a practical and pragmatic one. So I am not interested in any hypothetical Gods-eye view of the world. On the matter of what lies behind perceptions of continuity I am silent. In fact, in my entire philosophical system, only these statements precede the "perception of continuity": (1) I perceive that I think. (2) I perceive that my thoughts are intimately connected to memory, such that in thinking, I can recall memories of images, sounds, sensations, tastes, aromas, and emotions. (3) I perceive that I am constantly bombarded by sensory data, and that this sensory data possesses similar qualities to the data I can recall from memory. (4) I perceive that sensory data is not uniform, but differentiated, such that I can distinguish between parts of my sensory world, and such that these parts would seem to have a reasonably stable individual existence. So I shall pose the following definition: an "object" is a subset of my set of sensory data, that has a stable, individual existence. (5) I perceive that the sensory data I receive from an object is highly continuous, such that my present perceptions of the object agree with my memories of the object, and that my memories of the object agree with other memories of the object. So I shall pose the following definition: "reality" is the experience of continuity. You will notice in all of this, that I don't try to explain where these "perceptions" might come from. Such an explanation was not relevant to my goal of creating a pragmatic, practical philosophy. Nor, at this early stage, do I allow myself to stray very far beyond what I can directly perceive. There is no "Gods eye" view. I am not interested in an "absolute truth" that is beyond my human ability to perceive. I am only interested in "truths" that I can humanly know, or at least, humanly suspect. Let us continue: (6) I perceive that, on some rare occasions, my perception of memory disagrees with my current perception of sensory data. ...And that's what throws the spanner in the works. How do you procede from point #6? The "absolute truth" version of this discourse would say: "Let us imagine, therefore, an ideal point of view where point #6 is never the case." In a religious philosophy, this ideal point of view would be attributed to god. Personally, I am neither an idealist (in the sense given above) nor a theist. I would prefer that the discourse continue from my human point of view, rather than the ideal point of view. Why? Because I can't step outside of myself, and I can't really see anything from any other point of view than my own. Of course, you are all free to speculate about ideal viewpoints. You can say that they "exist" if you want, and I can't deny it. All I can say, is that I cannot put myself into that ideal position, so I cannot pretend that any statement I make is immune from point #6. Since I perceive that you are all human beings, like I am, I suspect that you are not immune from point #6 either. Now please (please!) don't write to me about the above paragraph saying things like: "Is that an absolute statement?" or "Do you realise that you have made a deduction, and that this deduction is based on absolutely true axioms?" The reasons why I choose to set certain rules for this exercise are not relevent to the exercise itself. The rules and underlying assumptions are arbitrary. They are based on certain suspicions that I have, but they are still arbitrary, nonetheless. I assume perception, a priori. I don't try to explain what it is, or how it works, because I deem that irrelevant to the exercise. Similarly, I have made the arbitrary rule that I may not step outside of my own point of view. I have also made the arbitrary rule that I shall not assume the prior truth of other philosophical abstractions in this exercise. If you don't like these assumptions, what can I do but shrug my shoulders? If you don't like mine, then write your own philosophical discourse. The seventh point of my philosophical discourse goes like this: (7) Because of #5, I may conclude that whenever I perceive an object, my perception will agree with past perceptions of the object. But because of #6 I can conclude that my anticipation of future perceptions may fail. So I pose the following definition: "uncertainty" is the possibility that an anticipated perception is incontinuous with the actual perception, and therefore, not real. |
04-01-2002, 06:16 PM | #20 |
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Actually, now that I come to look back at that, I perceive that there is an invisible point #0 that I left out.
(0) I am, and my state of being is perceptual. I think that will bring my assumption of perception a bit more out into the open. |
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